Assignment 1 Due: 11:59pm on Wednesday, February 5, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 1.6 Part A Determine the sign (positive or negative) of the position for the particle in the figure. ANSWER: Correct Part B Determine the sign (positive or negative) of the velocity for the particle in the figure. ANSWER: Correct Positive Negative Negative Positive

Assignment 2 Due: 11:59pm on Wednesday, February 12, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 2.6 Part A The figure shows the position-versus-time graph for a moving object. At which lettered point or points: Is the object moving the slowest? Is the object moving the fastest? Is the object at rest? Drag the appropriate items to their respective bins. ANSWER:

Chapter 3 Practice Problems (Practice – no credit) Due: 11:59pm on Wednesday, February 12, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Tactics Box 3.1 Determining the Components of a Vector Learning Goal: To practice Tactics Box 3.1 Determining the Components of a Vector. When a vector is decomposed into component vectors and parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This tactics box describes how to determine the x component and y component of vector , denoted and . TACTICS BOX 3.1 Determining the components of a vector The absolute value of the x component is the magnitude of the 1. component vector . 2. The sign of is positive if points in the positive x direction; it is negative if points in the negative x direction. 3. The y component is determined similarly. Part A What is the magnitude of the component vector shown in the figure? Express your answer in meters to one significant figure. A A x A y A Ax Ay |Ax| Ax A x Ax A x A x Ay A x ANSWER: Answer Requested Part B What is the sign of the y component of vector shown in the figure? ANSWER: Correct Part C Now, combine the information given in the tactics box above to find the x and y components, and , of vector shown in the figure. |Ax| = 5 m Ay A positive negative Bx By B Express your answers, separated by a comma, in meters to one significant figure. ANSWER: Correct Vector Components–Review Learning Goal: To introduce you to vectors and the use of sine and cosine for a triangle when resolving components. Vectors are an important part of the language of science, mathematics, and engineering. They are used to discuss multivariable calculus, electrical circuits with oscillating currents, stress and strain in structures and materials, and flows of atmospheres and fluids, and they have many other applications. Resolving a vector into components is a precursor to computing things with or about a vector quantity. Because position, velocity, acceleration, force, momentum, and angular momentum are all vector quantities, resolving vectors into components is the most important skill required in a mechanics course. The figure shows the components of , and , along the x and y axes of the coordinate system, respectively. The components of a vector depend on the coordinate system’s orientation, the key being the angle between the vector and the coordinate axes, often designated . Bx, By = -2,-5 m, m F Fx Fy Part A The figure shows the standard way of measuring the angle. is measured to the vector from the x axis, and counterclockwise is positive. Express and in terms of the length of the vector and the angle , with the components separated by a comma. ANSWER: Fx Fy F Fx, Fy = Fcos, Fsin Correct In principle, you can determine the components of any vector with these expressions. If lies in one of the other quadrants of the plane, will be an angle larger than 90 degrees (or in radians) and and will have the appropriate signs and values. Unfortunately this way of representing , though mathematically correct, leads to equations that must be simplified using trig identities such as and . These must be used to reduce all trig functions present in your equations to either or . Unless you perform this followup step flawlessly, you will fail to recoginze that , and your equations will not simplify so that you can progress further toward a solution. Therefore, it is best to express all components in terms of either or , with between 0 and 90 degrees (or 0 and in radians), and determine the signs of the trig functions by knowing in which quadrant the vector lies. Part B When you resolve a vector into components, the components must have the form or . The signs depend on which quadrant the vector lies in, and there will be one component with and the other with . In real problems the optimal coordinate system is often rotated so that the x axis is not horizontal. Furthermore, most vectors will not lie in the first quadrant. To assign the sine and cosine correctly for vectors at arbitrary angles, you must figure out which angle is and then properly reorient the definitional triangle. As an example, consider the vector shown in the diagram labeled “tilted axes,” where you know the angle between and the y axis. Which of the various ways of orienting the definitional triangle must be used to resolve into components in the tilted coordinate system shown? (In the figures, the hypotenuse is orange, the side adjacent to is red, and the side opposite is yellow.) F /2 cos() sin() F sin(180 + ) = −sin() cos(90 + ) = −sin() sin() cos() sin(180 + ) + cos(270 − ) = 0 sin() cos() /2 F |F| cos() |F| sin() sin() cos() N N N Indicate the number of the figure with the correct orientation. Hint 1. Recommended procedure for resolving a vector into components First figure out the sines and cosines of , then figure out the signs from the quadrant the vector is in and write in the signs. Hint 2. Finding the trigonometric functions Sine and cosine are defined according to the following convention, with the key lengths shown in green: The hypotenuse has unit length, the side adjacent to has length , and the cos() side opposite has length . The colors are chosen to remind you that the vector sum of the two orthogonal sides is the vector whose magnitude is the hypotenuse; red + yellow = orange. ANSWER: Correct Part C Choose the correct procedure for determining the components of a vector in a given coordinate system from this list: ANSWER: sin() 1 2 3 4 Correct Part D The space around a coordinate system is conventionally divided into four numbered quadrants depending on the signs of the x and y coordinates . Consider the following conditions: A. , B. , C. , D. , Which of these lettered conditions are true in which the numbered quadrants shown in ? Write the answer in the following way: If A were true in the third quadrant, B in the second, C in the first, and D in the fourth, enter “3, 2, 1, 4” as your response. ANSWER: Align the adjacent side of a right triangle with the vector and the hypotenuse along a coordinate direction with as the included angle. Align the hypotenuse of a right triangle with the vector and an adjacent side along a coordinate direction with as the included angle. Align the opposite side of a right triangle with the vector and the hypotenuse along a coordinate direction with as the included angle. Align the hypotenuse of a right triangle with the vector and the opposite side along a coordinate direction with as the included angle. x > 0 y > 0 x > 0 y < 0 x < 0 y > 0 x < 0 y < 0 Correct Part E Now find the components and of in the tilted coordinate system of Part B. Express your answer in terms of the length of the vector and the angle , with the components separated by a comma. ANSWER: Answer Requested ± Resolving Vector Components with Trigonometry Often a vector is specified by a magnitude and a direction; for example, a rope with tension exerts a force of magnitude in a direction 35 north of east. This is a good way to think of vectors; however, to calculate results with vectors, it is best to select a coordinate system and manipulate the components of the vectors in that coordinate system. Nx Ny N N Nx, Ny = −Nsin(),Ncos() T T Part A Find the components of the vector with length = 1.00 and angle =10.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. Hint 1. What is the x component? Look at the figure shown. points in the positive x direction, so is positive. Also, the magnitude is just the length . ANSWER: Correct Part B Find the components of the vector with length = 1.00 and angle =15.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. A a A x Ax |Ax| OL = OMcos() A = 0.985,0.174 B b Hint 1. What is the x component? The x component is still of the same form, that is, . ANSWER: Correct The components of still have the same form, that is, , despite 's placement with respect to the y axis on the drawing. Part C Find the components of the vector with length = 1.00 and angle 35.0 as shown. Enter the x component followed by the y component, separated by a comma. Hint 1. Method 1: Find the angle that makes with the positive x axis Angle = 0.611 differs from the other two angles because it is the angle between the vector and the y axis, unlike the others, which are with respect to the x axis. What is the angle that makes with the positive x axis? Express your answer numerically in degrees. ANSWER: Hint 2. Method 2: Use vector addition Look at the figure shown. Lcos() B = 0.966,0.259 B (Lcos(), Lsin()) B C c = C C 125 1. . 2. . 3. , the x component of is negative, since points in the negative x direction. Use this information to find . Similarly, find . ANSWER: Answer Requested ± Vector Addition and Subtraction In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors , , and . Calculate the following, and express your answers as ordered triplets of values separated by commas. Part A ANSWER: Correct C = C + x C y |C | = length(QR) = c sin() x Cx C C x Cx Cy C = -0.574,0.819 A = (1, 0,−3) B = (−2, 5, 1) C = (3, 1, 1) A − B = 3,-5,-4 Part B ANSWER: Correct Part C ANSWER: Correct Part D ANSWER: Correct B − C = -5,4,0 −A + B − C = -6,4,3 3A − 2C = -3,-2,-11 Part E ANSWER: Correct Part F ANSWER: Correct Video Tutor: Balls Take High and Low Tracks First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A −2A + 3B − C = -11,14,8 2A − 3(B − C) = 17,-12,-6 Consider the video demonstration that you just watched. Which of the following changes could potentially allow the ball on the straight inclined (yellow) track to win? Ignore air resistance. Select all that apply. Hint 1. How to approach the problem Answers A and B involve changing the steepness of part or all of the track. Answers C and D involve changing the mass of the balls. So, first you should decide which of those factors, if either, can change how fast the ball gets to the end of the track. ANSWER: Correct If the yellow track were tilted steeply enough, its ball could win. How might you go about calculating the necessary change in tilt? Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. A. Increase the tilt of the yellow track. B. Make the downhill and uphill inclines on the red track less steep, while keeping the total distance traveled by the ball the same. C. Increase the mass of the ball on the yellow track. D. Decrease the mass of the ball on the red track.

Chapter 3 Practice Problems (Practice – no credit) Due: 11:59pm on Wednesday, February 12, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Tactics Box 3.1 Determining the Components of a Vector Learning Goal: To practice Tactics Box 3.1 Determining the Components of a Vector. When a vector is decomposed into component vectors and parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This tactics box describes how to determine the x component and y component of vector , denoted and . TACTICS BOX 3.1 Determining the components of a vector The absolute value of the x component is the magnitude of the 1. component vector . 2. The sign of is positive if points in the positive x direction; it is negative if points in the negative x direction. 3. The y component is determined similarly. Part A What is the magnitude of the component vector shown in the figure? Express your answer in meters to one significant figure. A A x A y A Ax Ay |Ax| Ax A x Ax A x A x Ay A x

Chapter 05 Reading Questions Due: 11:59pm on Friday, May 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Chapter 5 Reading Quiz Question 1 Part A In the second stage of the demographic transition, called the mortality transition, the death rate _____ while the birth rate _____. ANSWER: Chapter 5 Reading Quiz Question 2 Part A About a century ago, the population in Latin America moved from an agricultural to an urban-industrial base. During this period birth rates _____, death rates _____, and the overall population _____. ANSWER: Chapter 5 Reading Quiz Question 16 Part A Over the course of human history, the greatest increases in human populations have been due to_____. ANSWER: increases, decreases decreases, decreases decreases, remains high or increases increases, remains high or increases stayed about the same, decreased, and the population grew even faster increased greatly, increased, declined decreased dramatically, decreased, declined stayed about the same, increased, increased Chapter 05 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 1 of 6 5/21/2014 8:00 PM Chapter 5 Reading Quiz Question 4 Part A Compared to women in the United States, women in poor countries such as Ethiopia typically have _____ children at _____ age. ANSWER: Chapter 5 Reading Quiz Question 18 Part A Women in two developed countries have similar total fertility rates of 3.5. However, women in country A typically have their children about 2 years earlier than women in country B. How will the populations of the two countries compare? ANSWER: Chapter 5 Reading Quiz Question 19 Part A Overall population growth rates are most likely to be highest when the median age of a population is _____ and a country is in stage _____ of the demographic transition. ANSWER: improved medicine improved water supplies discovery of new land increased food production fewer, an older more, a younger more, an older fewer, a younger The population of country B will increase faster than country A. The population of country A will increase but the population of country B will decline. The population of country A will increase faster than country B. The populations of both countries will be stable, with similar totals and little increase or decrease. Chapter 05 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 2 of 6 5/21/2014 8:00 PM Chapter 5 Reading Quiz Question 20 Part A An age-structure diagram of a poor country in stage 1 of the demographic transition will be closest to the shape of _____. ANSWER: Chapter 5 Reading Quiz Question 8 Part A Predictions about global growth rates have been difficult because of changes in human values and behavior largely based upon _____. ANSWER: Chapter 5 Reading Quiz Question 9 Part A Because human suffering _____ as the human population approaches its carrying capacity, sustainability of the global human population must be _____ the carrying capacity of the Earth. ANSWER: older, 1 younger, 4 older, 3 younger, 2 the letter O, widest in the middle a pyramid, with a broad base and narrow top the letter V, widest at the top column, with even width from top to bottom shifting weather patterns increasing abilities to travel between countries the spread of infectious disease economic development Chapter 05 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 3 of 6 5/21/2014 8:00 PM Chapter 5 Reading Quiz Question 10 Part A The IPAT formula is used to estimate the _____. ANSWER: Chapter 5 Reading Quiz Question 12 Part A If everyone in the world had the ecological footprint of people currently living in the United States and Canada, the world would _____. ANSWER: Chapter 5 Reading Quiz Question 22 Part A If the population of the United States continues to grow and consumption levels also increase, we expect that the _____. ANSWER: increases, below decreases, above increases, above decreases, below birth rate of a population shift from one stage to another in the demographic transition age structure of a population ecological footprint of a society have just enough biocapacity without any additional population growth exceed its biocapacity by 40% still have enough biocapacity for 20% more humans exceed its biocapacity by five times over Chapter 05 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 4 of 6 5/21/2014 8:00 PM Chapter 5 Reading Quiz Question 24 Part A Given the increasing global population and increased rates of consumption in developing countries, the most likely avenue to sustainability is _____. ANSWER: Chapter 5 Reading Quiz Question 13 Part A Which one of the following typically contributes to population growth? ANSWER: Chapter 5 Reading Quiz Question 14 Part A Members of the neo-Malthusian movement advocated for _____. ANSWER: ecological footprint will eventually exceed the biocapacity of the environment biocapacity will eventually exceed the ecological footprint of the environment United States will eventually become an ecological debtor ecological debt of the United States will continue to increase more efficient use of natural resources the discovery of ways to dramatically increase the global biocapacity to have developed countries use more natural resources from developing countries increase our reliance upon fossil fuels better education empowerment of women high infant mortality economic development Chapter 05 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 5 of 6 5/21/2014 8:00 PM Chapter 5 Reading Quiz Question 15 Part A China, Mexico, and India have all made progress in reducing the population growth rates in their countries by adopting policies that encourage _____. ANSWER: Chapter 5 Reading Quiz Question 7 Part A Malthus found that populations in the American colonies were increasing _____ than populations on the European continent due to _____. ANSWER: Score Summary: Your score on this assignment is 0.0%. You received 0 out of a possible total of 17 points. increasing population size to support greater economic development birth control to limit population growth greater use of natural resources to increase the biocapacity of Earth to support a growing human population greater conservation of natural resources to limit the environmental impact of a growing human population limits on family size women to work only inside of their homes women to start having children at a younger age couples to marry earlier faster, no political conflicts or wars faster, greater resources were available in the American colonies slower, fewer resources were available in the American colonies slower, greater disease in the American colonies Chapter 05 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 6 of 6 5/21/2014 8:00 PM

TEXT The sole text is Daniel Bonevac’s Today’s Moral Issues. This is an extremely accessible work that organizes the subject matter of ethics into well-structured units involving both general principles and focused ethical dilemmas. The instructor will guide the students through the pertinent readings and discussion topics. Exam #3: WAR ECONOMIC EQUALITY 1. Aquinas 5. Mill 2. Grotius 6. Hospers 3. Clausewitz 7. Anderson 4. Gandhi CONCERNING THE SHORT PAPER Choose one of our dilemma topics from our book as the focus of your short paper. If you have another topic in mind, please consult with me for permission. —length: 4 to 5 pages — format: typed —number of points: 10 — submission via Bb, under “Assignments” — Format: Microsoft Word — Line Spacing: Double-Spaced —Print: Black The following is merely a suggestion for the organization of the paper, but it might be useful as an indication of how it could look: a) Initial statement of your position concerning the moral dilemma; how to resolve it, how you plan to argue for/against it. b) Amplification of your position; your main points or position. c) Backup: some cited references and supporting evidence for your position. d) Your criticisms of alternative or contrary points of view. e) Your conclusion/summing up. Plagiarism is a serious breach of academic integrity. If you submit plagiarized materials you will receive a zero on the assignment. If you need an extension of the due date for the paper, please consult with me.

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Use the link provided to answer the questions below. http://www.worlddialogue.org/content.php?id=384 According to the article, what was President George W. Bush’s main rationale for going to war with Iraq? A. Bush believed that by promoting democracy, we promote peace around the world. B. Bush believed that Iraq was a key player in the global drug trade. C. Bush feared Osama bin Laden would assume power in Iraq. D. Intelligence reports showed Iraq was planning to attack Afghanistan. E. Bush had no opinion about invading Iraq. What is the democratic peace theory? A. the theory that indicates that democracy will inevitably spread and we should assist it peacefully B. the theory that economic growth leads to a peaceful democratic state C. the theory that democracies tend not to fight one another D. the theory that the key to a successful democratic transition is through a peaceful transfer of power E. the theory that peace and democracy are actually inconsistent with one another What did Mansfield and Syder conclude happens during the initial phases of democratization? A. Newly democratized countries are incapable of holding independent elections. B. Citizens are more engaged in politics and willing to be peaceful. C. New democracies are the strongest democracies in the world. D. Other countries are more likely to form alliances with new democracies. E. Newly democratized countries become more aggressive and warlike, not less. New democracies are more likely to elect which of the following types of parties into office? A. socialists B. religious extremists C. the country’s elite and wealthy class D. people who personify “the average Joe” E. the largest, most prominent parties According to Mansfield and Snyder’s prescription, what should the United States do with democratizing states? A. provide an international military force to ensure peace B. keep a close eye and replace bad leaders if necessary C. make certain that reforms are implemented in the right order D. strengthen international awareness of democratizing states so that peaceful states can arm themselves E. attempt to push through elections as soon as possible above all else Watch the video below, and then answer the questions below. To save your answers, click the Save to Notebook button above. http://www.youtube.com/watch?v=796LfXwzIUk According to Joseph Nye, what is power transition? A. a change of power among states B. a change of power among presidents C. a change of power within the European Union or other leading organizations D. a change of power within cultures E. a change of power to non-state actors How does Nye define power diffusion? A. a change of power among states B. a change of power in regions C. a change of power within cultures D. a change of power from states to non-state actors E. a change of power from non-state actors to states Which of the following is an example of a non-state actor given by Nye? A. Iranian president Mahmoud Ahmadinejad B. Oxfam C. the former USSR D. socialism E. the mayor of Tehran Why does Nye claim it is important to be cautious of power projections? A. Simple projections don’t tell us much about power transition. B. History is not linear. C. Simple projections tend to focus soley on GDP. D. Simple projections don’t tell you anything about military or soft power. E. all of these options Nye describes a three-dimensional chess game as a metaphor for modern-day power distribution. What is the top board? A. economic power among states B. military power among states C. power among state leaders D. the deciding board for the other two boards E. the board where Kasparov faces off against the computer What is the middle board in Nye’s chess game metaphor? A. non-state actors B. a metaphor for the international underground economy C. military power among states D. economic power among states E. political power among states What is the bottom board in Nye’s chess game metaphor? A. transnational relations B. things that cross borders outside government control C. a place where power is chaotically distributed D. an area where things cross borders outside the control of governments E. all of these options What is the difference between a positive-sum game and a zero-sum game? A. A positive-sum game is when one person has all the power and a zero-sum game is when power is evenly distributed. B. A positive-sum game is a two-player power game and a zero-sum game is a one-player power game. C. A positive-sum game where my gain is your gain and a zero-sum game is my win and your loss. D. A postive-sum game is when you bet and win and a zero-sum game is when you bet and lose. E. A positive-sum game is like Tetris and a zero-sum game is like Super Mario Brothers. Nye quotes Hillary Clinton, describing her foreign policy agenda as utilizing “smart power.” What does this mean? A. Smart power addresses the two great power shifts in the 21st century. B. Smart power is “using all the tools in our toolbox.” C. Smart power combines both hard and soft power. D. Smart power reflects a new narrative of dealing with power. E. all of these options

Chapter 1 Practice Problems (Practice – no credit) Due: 11:59pm on Wednesday, February 5, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Curved Motion Diagram The motion diagram shown in the figure represents a pendulum released from rest at an angle of 45 from the vertical. The dots in the motion diagram represent the positions of the pendulum bob at eleven moments separated by equal time intervals. The green arrows represent the average velocity between adjacent dots. Also given is a “compass rose” in which directions are labeled with the letters of the alphabet. Part A What is the direction of the acceleration of the object at moment 5? Enter the letter of the arrow with this direction from the compass rose in the figure. Type Z if the acceleration vector has zero length. You did not open hints for this part. ANSWER: Incorrect; Try Again Part B What is the direction of the acceleration of the object at moments 0 and 10? Enter the letters corresponding to the arrows with these directions from the compass rose in the figure, separated by commas. Type Z if the acceleration vector has zero length. You did not open hints for this part. ANSWER: Incorrect; Try Again PSS 1.1 Motion Diagrams Learning Goal: To practice Problem-Solving Strategy 1.1 for motion diagram problems. A car is traveling with constant velocity along a highway. The driver notices he is late for work, so he stomps down on the gas pedal and the car begins to speed up. The car has just achieved double its directions at time step 0, time step 10 = initial velocity when the driver spots a police officer behind him and applies the brakes. The car then slows down, coming to rest at a stoplight ahead. Draw a complete motion diagram for this situation. PROBLEM-SOLVING STRATEGY 1.1 Motion diagrams MODEL: Represent the moving object as a particle. Make simplifying assumptions when interpreting the problem statement. VISUALIZE: A complete motion diagram consists of: The position of the object in each frame of the film, shown as a dot. Use five or six dots to make the motion clear but without overcrowding the picture. More complex motions may need more dots. The average velocity vectors, found by connecting each dot in the motion diagram to the next with a vector arrow. There is one velocity vector linking each set of two position dots. Label the row of velocity vectors . The average acceleration vectors, found using Tactics Box 1.3. There is one acceleration vector linking each set of two velocity vectors. Each acceleration vector is drawn at the dot between the two velocity vectors it links. Use to indicate a point at which the acceleration is zero. Label the row of acceleration vectors . Model It is appropriate to use the particle model for the car. You should also make some simplifying assumptions. v 0 a Part A The car’s motion can be divided into three different stages: its motion before the driver realizes he’s late, its motion after the driver hits the gas (but before he sees the police car), and its motion after the driver sees the police car. Which of the following simplifying assumptions is it reasonable to make in this problem? During each of the three different stages of its motion, the car is moving with constant A. acceleration. B. During each of the three different stages of its motion, the car is moving with constant velocity. C. The highway is straight (i.e., there are no curves). D. The highway is level (i.e., there are no hills or valleys). Enter all the correct answers in alphabetical order without commas. For example, if statements C and D are correct, enter CD. ANSWER: Correct In addition to the assumptions listed above, in the rest of this problem assume that the car is moving in a straight line to the right. Visualize Part B In the three diagrams shown to the left, the position of the car at five subsequent instants of time is represented by black dots, and the car’s average velocity is represented by green arrows. Which of these diagrams best describes the position and the velocity of the car before the driver notices he is late? ANSWER: Correct Part C Which of the diagrams shown to the left best describes the position and the velocity of the car after the driver hits the gas, but before he notices the police officer? ANSWER: Correct A B C A B C Part D Which of the diagrams shown to the left best describes the position and the velocity of the car after the driver notices the police officer? ANSWER: Correct Part E Which of the diagrams shown below most accurately depicts the average acceleration vectors of the car during the events described in the problem introduction? ANSWER: A B C Correct You can now draw a complete motion diagram for the situation described in this problem. Your diagram should look like this: Measurements in SI Units Familiarity with SI units will aid your study of physics and all other sciences. Part A What is the approximate height of the average adult in centimeters? Hint 1. Converting between feet and centimeters The distance from your elbow to your fingertips is typically about 50 . A B C cm ANSWER: Correct If you’re not familiar with metric units of length, you can use your body to develop intuition for them. The average height of an adult is 5 6.4 . The distance from elbow to fingertips on the average adult is about 50 . Ten (1 ) is about the width of this adult’s little finger and 10 is about the width of the average hand. Part B Approximately what is the mass of the average adult in kilograms? Hint 1. Converting between pounds and kilograms Something that weighs 1 has a mass of about . ANSWER: Correct Something that weighs 1 has a mass of about . This is a useful conversion to keep in mind! ± A Trip to Europe 100 200 300 cm cm cm feet inches cm mm cm cm pound 1 kg 2 80 500 1200 kg kg kg pound (1/2) kg Learning Goal: To understand how to use dimensional analysis to solve problems. Dimensional analysis is a useful tool for solving problems that involve unit conversions. Since unit conversion is not limited to physics problems but is part of our everyday life, correct use of conversion factors is essential to working through problems of practical importance. For example, dimensional analysis could be used in problems involving currency exchange. Say you want to calculate how many euros you get if you exchange 3600 ( ), given the exchange rate , that is, 1 to 1.20 . Begin by writing down the starting value, 3600 . This can also be written as a fraction: . Next, convert dollars to euros. This conversion involves multiplying by a simple conversion factor derived from the exchange rate: . Note that the “dollar” unit, , should appear on the bottom of this conversion factor, since appears on the top of the starting value. Finally, since dollars are divided by dollars, the units can be canceled and the final result is . Currency exchange is only one example of many practical situations where dimensional analysis may help you to work through problems. Remember that dimensional analysis involves multiplying a given value by a conversion factor, resulting in a value in the new units. The conversion factor can be the ratio of any two quantities, as long as the ratio is equal to one. You and your friends are organizing a trip to Europe. Your plan is to rent a car and drive through the major European capitals. By consulting a map you estimate that you will cover a total distance of 5000 . Consider the euro-dollar exchange rate given in the introduction and use dimensional analysis to work through these simple problems. Part A You select a rental package that includes a car with an average consumption of 6.00 of fuel per 100 . Considering that in Europe the average fuel cost is 1.063 , how much (in US dollars) will you spend in fuel on your trip? Express your answer numerically in US dollars to three significant figures. You did not open hints for this part. ANSWER: US dollars USD 1 EUR = 1.20 USD euro US dollars USD 3600 USD 1 1.00 EUR 1.20 USD USD USD ( )( ) = 3000 EUR 3600 USD 1 1.00 EUR 1.20 USD km liters km euros/liter Part B How many gallons of fuel would the rental car consume per mile? Express your answer numerically in gallons per mile to three significant figures. You did not open hints for this part. ANSWER: Part C This question will be shown after you complete previous question(s). Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. Cost of fuel = USD gallons/mile